The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  3  0  9 24 21  3 15 24  9  9 15 18 12 15 21 24 21 18 12  9 24 12  6 15  0  0 21 12 15 21 24 12  6 18 18  6 15 21 12 24  6  0  0  6 12 21 18  0  6 18  3  3  0 18 18 21 12 24 15 15 24  9  3  9 24  0 12  3 18 21 15  9  9  3  3  9  3  6  6  6  0 18 21  3  9
 0  0  3 15  9  6  3 21 15  0  6 18 21 24 12 12 24  0 24  3  9 21 18  6  0 18 21 18 12  6 24 18 15 12 15  3 24 15 15  9  3  9 12  9  0  6 21  9  6  3 12  9 21 24 18  6  3  0  0  9  3  6 21 15  3 12 15 21  6  0  9 24 12 24 24 12 18 18 18 21 15  0 21 15  3  0

generates a code of length 86 over Z27 who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+42x^168+36x^169+54x^170+80x^171+1710x^172+108x^173+114x^174+36x^175+4x^177+2x^258

The gray image is a code over GF(3) with n=774, k=7 and d=504.
This code was found by Heurico 1.16 in 0.294 seconds.